Each metric is a subclass of BaseMetricLearner, which provides
default implementations for the methods metric, transformer, and
transform. Subclasses must provide an implementation for either
metric or transformer.

For an instance of a metric learner named foo learning from a set of
d-dimensional points, foo.metric() returns a d by d
matrix M such that a distance between vectors x and y is
expressed (x-y).dot(M).dot(x-y).

In the same scenario, foo.transformer() returns a d by d
matrix L such that a vector x can be represented in the learned
space as the vector x.dot(L.T).

For convenience, the function foo.transform(X) is provided for
converting a matrix of points (X) into the learned space, in which
standard Euclidean distance can be used.

Notes

If a recent version of the Shogun Python modular (modshogun) library
is available, the LMNN implementation will use the fast C++ version from
there. The two implementations differ slightly, and the C++ version is
more complete.